Advanced Calculus For Economics And Finance Theory And Methods 1st Edition Giulio Bottazzi by Giulio Bottazzi 9783031303159, 9783031303166, 3031303156, 3031303164 instant download after payment.

This is a book about advanced calculus and analysis.

"The idea is to teach the reader the appropriate language and notions about each topic so that they can understand where and how to look for more specific discussions should the need arise. The main criterion that drove the selection of topics is usability in applications, in particular, applications in economics and social sciences. This is why I have avoided almost entirely any geometric consideration, which is important in a course for hard scientists and engineers, and I have insisted on mathematical results mostly useful for optimisation theory and statistics. The two final appendices, on the initial value problem for systems of differential equations and on the Brower fixed-point theorem, exemplify two possible domains of application of the material covered in this book."

This textbook provides a comprehensive introduction to mathematical calculus. Written for advanced undergraduate and graduate students, it teaches the fundamental mathematical concepts, methods and tools required for various areas of economics and the social sciences, such as optimization and measure theory. The reader will be introduced to topological, metric and normed spaces, learning about numerical sequences, series, and differential and integral calculus. These concepts are introduced using the axiomatic approach as a tool for logical reasoning, consistency, and formalization of ideas. The book follows a theorem-proving approach, stressing the limitations of applying the different theorems, while providing thought-provoking counter-examples. Each chapter features exercises that facilitate learning and allow students to apply and test important concepts and tools.